### Almost Disturbance Decoupling for HOFA Nonlinear Systems with Strict-Feedback Form

WANG Na1, LIU Xiaoping1,2, LIU Cungen1, WANG Huanqing3, ZHOU Yucheng1

1. 1. School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan 250101, China;
2. Faculty of Engineering, Lakehead University, Thunder Bay, ON P7B 5E1, Canada;
3. The Department of Mathematics, Bohai University, Jinzhou 121013, China
• Received:2022-01-07 Revised:2022-01-20 Published:2022-04-13
• Contact: LIU Cungen. Email: littleeggs@sdjzu.edu.cn
• Supported by:
This research was supported by the Taishan Scholar Project of Shandong Province of China under Grant Nos. 2015162 and tsqn201812093.

WANG Na, LIU Xiaoping, LIU Cungen, WANG Huanqing, ZHOU Yucheng. Almost Disturbance Decoupling for HOFA Nonlinear Systems with Strict-Feedback Form[J]. Journal of Systems Science and Complexity, 2022, 35(2): 481-501.

The article is devoted to the almost disturbance decoupling problem for high-order fully actuated (HOFA) nonlinear systems with strict-feedback form. Using the full-actuation feature of high-order fully actuated systems and Lyapunov stability theory, a state feedback control law and virtual control laws are designed. The unknown disturbances are handled by almost disturbance decoupling (ADD) method. Finally, the effectiveness of the control strategy is verified by stability analysis and simulation.
 [1] Duan G R, High-order system approaches: Part I. Fully actuated systems and parametric designs, Acta Automatica Sinica, 2020, 46(7): 1333–1345.[2] Duan G R, High-order fully actuated system approaches: Part I. Models and basic procedure, International Journal of Systems Science, 2021, 52(2): 422–435.[3] Duan G R, High-order system approaches: Part II. Controllability and full-actuation, Acta Automatica Sinica, 2020, 46(8): 1571–1581.[4] Duan G R, High-order fully-actuated system approaches: Part II. Generalized strict-feedback systems, International Journal of Systems Science, 2021, 52(3): 437–454.[5] Duan G R, High-order fully-actuated system approaches: Part III. Robust control and high-order backstepping, International Journal of Systems Science, 2021, 52(5): 952–971.[6] Duan G R, High-order fully actuated system approaches: Part IV. Adaptive control and high-order backstepping, International Journal of Systems Science, 2021, 52(5): 972–989.[7] Duan G R, High-order fully actuated system approaches: Part V. Robust adaptive control, International Journal of Systems Science, 2021, 52(10): 2129–2143.[8] Duan G R, High-order fully-actuated system approaches: Part VI. Disturbance attenuation and decoupling, International Journal of Systems Science, 2021, 52(10): 2161–2181.[9] Duan G R, High-order fully-actuated system approaches: Part VII. Controllability, stabilisability and parametric designs, International Journal of Systems Science, 2021, 52(14): 3091–3114.[10] Duan G R, High-order fully-actuated system approaches: Part VIII. Optimal control with application in spacecraft attitude stabilisation, International Journal of Systems Science, 2021, 53(1): 54–73.[11] Duan G R, High-order fully-actuated system approaches: Part IX. Generalised PID control and model reference tracking, International Journal of Systems Science, 2021, DOI: 10.1080/00207721.2021.1970277.[12] Duan G R, High-order fully-actuated system approaches: Part X. Basics of discrete-time systems, International Journal of Systems Science, 2021, DOI: 10.1080/00207721.2021.1975848.[13] Duan G R, High-order system approaches –III. Super-observability and observer design, Acta Automatica Sinica, 2020, 46(9): 1885–1895.[14] Willems J C and Commault C, Disturbance decoupling by measurement feedback with stability or pole placement, SIAM Journal on Control & Optimization, 1981, 19(4): 490–504.[15] Basile G and Marro G, Controlled and Conditioned Invariants in Linear System Theory, Prentice Hall, Upper Saddle River, New Jersey, 1992.[16] Nijmeijer H and Schaft V A, Nonlinear Dynamical Control Systems, Springer, New York, 175, 1990.[17] Willems J, Almost invariant subspaces: An approach to high gain feedback design, Part I: Almost controlled invariant subspaces, IEEE Transactions on Automatic Control, 1981, 26(1): 235–252.[18] Marino R, Respondek W, and Schaft A, Almost disturbance decoupling for single-input singleoutput nonlinear systems, IEEE Transactions on Automatic Control, 1989, 34(9): 1013–1017.[19] Willand S and Willems J C, Almost disturbance decoupling with internal stability, IEEE Transactions on Automatic Control, 1989, 34: 277–286.[20] Fradkov A L, Miroshnik L V, and Nikiforov V O, Nonlinear and adaptive control of complex systems, Nonlinear and Adaptive Control of Complex Systems, 1999.[21] Chen B, Tong S C, and Liu X P, Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by ackstepping approach, Fuzzy Sets and Systems, 2007, 158(10): 1097–1125.[22] Tan Q Q, Li T, Song Z Y, et al., Output tracking control for generalized high-order nonlinear system with almost disturbance decoupling, International Journal of Control Automation and Systems, 2007, 15(6): 2570–2578.[23] Fu Y M, Wu A G, and Duan G R, Almost disturbance decoupling for a class of inherently nonlinear systems, International Journal of Control Automation and Systems, 2009, 7(2): 325–330.[24] Zhang Z Y, Liu X P, Liu Y, et al., Fixed-time almost disturbance decoupling of nonlinear timevarying systems with multiple disturbances and dead-zone input, Information Sciences: An International Journal, 2018, 450: 267–283.[25] Liu X P, Liu Y, Zhou Y C, et al., The finite-time almost disturbance decoupling for nonlinear systems, International Journal of Systems Science, 2018, 49(9–12): 2243–2256.[26] Liu X P, Zhao Y J, Wang C Y, et al., Almost disturbance decoupling for a class of fractional-order nonlinear systems with zero dynamics, Complexity, 2020, 1: 1–13.[27] Chen C C, Chien T L, and Wu C J, Simultaneous tracking and almost disturbance decoupling for nonlinear systems with uncertainties, Journal of the Chinese Institute of Engineers, Series A, 2004, 27(1): 23–24.[28] Liu X P, Jutan A, and Jutan S, Almost disturbance decoupling of MIMO nonlinear systems and application to chemical processes, Automatica, 2004, 40(3): 465–471.[29] Yang L and Jing Y W, Practical finite-time almost disturbance decoupling strategy for uncertain nonlinear systems, Nonlinear Dynamics, 2019, 95(3): 117–128.[30] Kang S, Nagamune R, Yan H, et al., Almost disturbance decoupling force control for the electrohydraulic load simulator with mechanical backlash, Mechanical Systems and Signal Processing, 2020, 135: 106400.[31] Chu H Y, Qian C J, Yang J Q, et al., Almost disturbance decoupling for a class of nonlinear systems via sampled-data output feedback control, International Journal of Robust and Nonlinear Control, 2016, 26(10): 2201–2215.[32] Yang J, Chen W H, Li S H, et al., Static disturbance-to-output decoupling for nonlinear systems with arbitrary disturbance relative degree, International Journal of Robust & Nonlinear Control, 2013, 23(5), DOI: 10.1002/rnc.1850.[33] Li C Y and Wang W, Fuzzy almost disturbance decoupling for MIMO nonlinear uncertain systems based on high-gain observer, Neurocomputing, 2013, 111: 104–114.[34] Zhong Z Z and Wang J C, Looper-tension almost disturbance decoupling control for hot strip finishing mill based on feedback linearization, IEEE Transactions on Industrial Electronics, 2011, 58(8): 3668–3679.[35] Chu H Y, Qian C J, Yang J Q, et al., Almost disturbance decoupling for a class of nonlinear systems via sampled-data output feedback control, International Journal of Robust and Nonlinear Control, 2016, 16(10): 2201–2215.[36] Isidori A and Astolfi A, Disturbance attenuation and H∞-control via measurement feedback in nonlinear systems, IEEE Transactions on Automatic Control, 1992, 37(9): 1283–1293.[37] Zhou K M, Doyle J C, and Glover K, Robust and Optimal Control, Prentice-Hall, Inc., Upper Saddle River, New Jersey, 1996.[38] Duan G R, Generalized Sylvester Equations: Unified Parametric Solutions, CRC Press, Boca Raton, 2015.[39] Chen W H, Disturbance observer based control for nonlinear systems, IEEE/ASME Transactions on Mechatronics, 2004, 9(4): 706–710.
 [1] LI Wuquan · KRSTIC Miroslav. Prescribed-Time Control of Stochastic Nonlinear Systems with Reduced Control Effort [J]. Journal of Systems Science and Complexity, 2021, 34(5): 1782-1800. [2] Jian Feng WEI;Yu Fan ZHANG. A NOTE ON NONLINEAR ROBUST H_∞ ALMOST DISTURBANCE DECOUPLING PROBLEM WITH STABILITY [J]. Journal of Systems Science and Complexity, 2002, 15(1): 35-042.
Viewed
Full text

Abstract